@elbaroni I used to be in the same boat as you not too long ago. This is what I've come to understand about recapping and capacitors:
capacitance is what matters: the
µf (microfarads) part. So you want to make sure that one is
equal to what you need. The Voltage part is the rated tolerance. This one can be equal to
or greater than what you need. So it's OK to put in a higher rated capacitor such as 47µf 20V in place of a 47µf 16V.
ESR isn't specified because it probably doesn't matter too much in this case. From what I've read, the lower the better.
Next is to just make sure that it's the right type of cap. Tantalums are good replacements for surface-mount caps. Axials are for a couple of the horizontal through-hole caps, and radials for the regular through-holes.
I just can't remember the type of capacitor, but there's one that LOOKS like an old electrolytic surface mount, but they're more reliable. They're also more expensive, but they'll keep the old-school look of the motherboard without using tantalums.